Recent Trends in Stochastic Partial Differential Equations: An Invariance Principle for some Reaction-Diffusion Equations with a Multiplicative Random Source
Presenter
November 17, 2025
Keywords:
- stochastic partial differential equations
- regularity structures
- paracontrolled calculus
- nonlinear dispersive equations
- Gibbs measures
- homogenization
- stochastic fluid dynamics
- quantum field theory
MSC:
- 60H15 - Stochastic partial differential equations (aspects of stochastic analysis)
Abstract
We establish a notion of universality for the parabolic An- derson model via an invariance principle for a wide family of parabolic stochastic partial differential equations. We then use this invariance principle in order to provide an asymptotic theory for a wide class of non-linear SPDEs. A novel ingredient of this invariance principle is the dissipativity of the underlying stochastic PDE.